Join- and-cut algorithm for self-avoiding walks with variable length and free endpoints |
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Authors: | Sergio Caracciolo Andrea Pelissetto AJan D Sokal |
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Institution: | (1) Scuola Normale Superiore and INFN-Sezione di Pisa, 56100 Pisa, Italy;(2) Department of Physics, Princeton University, 08544 Princeton, New Jersey;(3) Present address: Dipartimento di Fisica, Università degli Studi di Pisa, 56100 Pisa, Italy;(4) Department of Physics, New York University, 10003 New York, New York |
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Abstract: | We introduce a new Monte Carlo algorithm for generating self-avoiding walks of variable length and free endpoints. The algorithm works in the unorthodox ensemble consisting of all pairs of SAWs such that the total number of stepsN
tot in the two walks is fixed. The elementary moves of the algorithm are fixed-N (e.g., pivot) moves on the individual walks, and a novel join- and-cut move that concatenates the two walks and then cuts them at a random location. We analyze the dynamic critical behavior of the new algorithm, using a combination of rigorous, heuristic, and numerical methods. In two dimensions the autocorrelation time in CPU units grows as N 1.5, and the behavior improves in higher dimensions. This algorithm allows high-precision estimation of the critical exponent . |
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Keywords: | Self-avoiding walk polymer Monte Carlo join- and-cut algorithm pivot algorithm critical exponent |
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